System and methods for storing data encoded with error information in a storage medium are provided. A binary data and an encoded binary error signals are received. The encoded binary error signal includes information that represents occurrence of errors in the binary data signal. The binary data and encoded binary error signals are encoded to generate a binary codeword signal. Bits of the binary codeword signal that represent coding information and the binary data signal are extracted. The extracted bits of the binary codeword signal are stored in a first storage medium. The binary packed data signal is retrieved from the first storage device and decoded to recover the binary data signal and a syndrome. Error information corresponding to the encoded binary error signal may be determined based on the syndrome.